In order to look for the sign of the charge, you should think about in what direction it should excert the force. Since the two bottom charges are postive, the "push" the central charge upwards, which means that, in order to get null net force, you need de upper charge to push downwards on the central one. What does this tell you about the sign of the charge?

As for the amgnitude of the force, you are thinking the right way but you forgot something. The charges at the bottom are not aligned with the other ones, which means that the forces excerted by this charges won't be in a vertical line, but will at some angle different from zero with the vertical. However this two forces do have a vertical component. You should compute this, since this is the force the upper charge has to counter.

As you said, this time the sign would be possitive. However tou have overlookes a couple of things.

The triangle formed by the charges is not an equilateral one, so the angle is not 60º. Actually it doesn't matter the actual value of the angle, since you only want to know its cosine, but you already now the values of the three sides, so knowing the cosine is pretty straight forward. You are looking at the upper angle in that triangle so, the cosine should be 3/5.

On the other hand, you should also remember that there are 2 charges at the bottom so, if looked at what you did correctly, the force should be twice as much.